@article{0ee52a68f5f340bbb930274def7045d2,

title = "A harder-narasimhan theory for kisin modules",

abstract = "We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite at group schemes due to Fargues [La filtration de Harder-Narasimhan des sch-emas en groupes finis et plats, J. reine angew. Math. 645 (2010), 1-39]. We prove the tensor product theorem, in other words, that the tensor product of semistable objects is again semi-stable. We then apply the tensor product theorem to the study of Kisin varieties for arbitrary connected reductive groups.",

keywords = "Algebraic groups, Deformation theory, Finite at group schemes, Geometric invariant theory, P-adic hodge theory",

author = "Brandon Levin and Carl Wang-Erickson",

note = "Funding Information: We owe a debt to Laurent Fargues, as the in uence of his work will be clear to the reader. We also appreciate Jay Pottharst's exposition [Pot20] of the formal structure of HN-theory and thank him for making his manuscript available on arXiv. Likewise, we appreciate Daniel Halpern-Leistner's exposition in [Hal18] of results we needed to cull from geometric invariant theory. We thank Christophe Cornut for a very careful reading of the text and several detailed emails that helped us correct and refine the proofs in Section 3. We thank an anonymous referee for making us aware of the references [Kir84, Nes84] on geometric invariant theory. We thank Madhav Nori for helpful conversations. We would like to recognize the mathematics departments at the University of Chicago and Brandeis University for providing excellent working conditions as this project was carried out. Funding Information: C.W.E. thanks the AMS and the Simons Foundation for support for this project in the form of an AMS-Simons Travel Grant. Publisher Copyright: {\textcopyright} 2020 European Mathematical Society Publishing House.",

year = "2020",

doi = "10.14231/AG-2020-024",

language = "English (US)",

volume = "7",

pages = "645--795",

journal = "Algebraic Geometry",

issn = "2313-1691",

publisher = "European Mathematical Society Publishing House",

number = "6",

}